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Chapter 2: B. Basic Algebra 17
To check your work, you must first check to see if the equality holds true. Then
choose a number that is in the range of solutions to make sure the inequality is
also correct, as shown below. Check for the equality condition:
7
y + 30 51
8
7
24+ 30 = 51
8
21+ 30 = 51
51=
51
Part I.B
To check for the inequality condition, use a number in the solution range. Recall
that the solution to the example was y 24. Here we arbitrarily choose 40 to perform
the check:
7
y + 30 51
8
7
40+ 30 51
8
35+ 30 51
65 51
Solving Inequalities with Negatively Signed Values
Be careful when solving an inequality by multiplying or dividing both sides by
a negative number—the inequality sign reverses! Checking your work after solving
an inequality is very important to make sure that the sign of your answer is
correct. For example,
Check for the equality condition:
7x
+ 4
25
7x
+ 44254
7x
21
7x
÷ 7 21÷ 7
x 3.
7x
+ 4
25
( 7x
3)+ 4=
25
21+ 4 = 25
25 = 25